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Matrix element evaluation in the unitary group approach to the electron correlation problem
Author(s) -
Shavitt Isaiah
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560140803
Subject(s) - unitary group , hamiltonian matrix , unitary state , wave function , unitary matrix , factorization , hamiltonian (control theory) , formalism (music) , generator matrix , matrix (chemical analysis) , computational chemistry , mathematics , configuration interaction , matrix representation , algebra over a field , quantum mechanics , group (periodic table) , physics , chemistry , pure mathematics , symmetric matrix , algorithm , eigenvalues and eigenvectors , mathematical optimization , law , chromatography , political science , art , excited state , decoding methods , visual arts , musical
Computationally effective formulations are presented for the evaluation of matrix elements of unitary group generators and products of generators between Gelfand states. These matrix elements are the coefficients of the orbital integrals in the expressions for the Hamiltonian matrix elements in the Gelfand basis, and as such are the key elements in any application of the unitary group approach to wave‐function calculations. The present formulations, which, like previous analyses, result in a simple factorization of the generator matrix elements, are based on a graphical representation of the Gelfand basis, and do not require orbital permutations or an interpretation of the Gelfand states in terms of Young tableaus. It is shown that the resulting formalism can lead to very efficient procedures for “direct” configuration‐interaction calculations, and probably also for perturbation‐theory treatments.